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Some foundations for multiplicative habits models

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  • Hiraguchi, Ryoji

Abstract

Consumption models with multiplicative habits are becoming increasingly popular. However, mathematical foundations of such models are incomplete because the utility function with multiplicative habits is not concave. This paper shows that an optimal consumption path exists and it satisfies the first order conditions. The paper also shows that when the production function is linear, consumption growth rate along the optimal path converges to a positive constant under several parametric restrictions.

Suggested Citation

  • Hiraguchi, Ryoji, 2008. "Some foundations for multiplicative habits models," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 873-884, September.
    • Handle: RePEc:eee:jmacro:v:30:y:2008:i:3:p:873-884
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    1. Jody Overland & Christopher D. Carroll & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, June.
    2. Alonso-Carrera, Jaime & Caballe, Jordi & Raurich, Xavier, 2005. "Growth, habit formation, and catching-up with the Joneses," European Economic Review, Elsevier, vol. 49(6), pages 1665-1691, August.
    3. Carroll, Christopher D & Overland, Jody & Weil, David N, 1997. "Comparison Utility in a Growth Model," Journal of Economic Growth, Springer, vol. 2(4), pages 339-367, December.
    4. Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, September.
    5. Francisco Alvarez-Cuadrado & Goncalo Monteiro & Stephen J. Turnovsky, 2004. "Habit Formation, Catching Up with the Joneses, and Economic Growth," Journal of Economic Growth, Springer, vol. 9(1), pages 47-80, March.
    6. Takashi Kamihigashi, 2002. "A simple proof of the necessity of the transversality condition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 427-433.
    7. Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August.
    8. Carroll, Christopher D., 2000. "Solving consumption models with multiplicative habits," Economics Letters, Elsevier, vol. 68(1), pages 67-77, July.
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    Cited by:

    1. Hiraguchi, Ryoji, 2011. "A two sector endogenous growth model with habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 430-441, April.
    2. Gómez, Manuel A. & Monteiro, Goncalo, 2015. "Internal habits in an endogenous growth model with elastic labor supply," Economic Modelling, Elsevier, vol. 51(C), pages 583-595.
    3. Gomez Suarez, Manuel A., 2008. "Utility and production externalities, equilibrium efficiency and leisure specification," Journal of Macroeconomics, Elsevier, vol. 30(4), pages 1496-1519, December.
    4. Gómez Manuel A., 2010. "Endogenous Growth, Habit Formation and Convergence Speed," The B.E. Journal of Macroeconomics, De Gruyter, vol. 10(1), pages 1-32, January.
    5. repec:ebl:ecbull:eb-17-00806 is not listed on IDEAS
    6. van den Bijgaart, Inge, 2016. "Essays in environmental economics and policy," Other publications TiSEM 298bee2a-cb08-4173-9fe1-8, Tilburg University, School of Economics and Management.
    7. Manuel Gómez, 2010. "A note on external habits and efficiency in the AK model," Journal of Economics, Springer, vol. 99(1), pages 53-64, February.
    8. van den Bijgaart, I.M., 2017. "Too slow a change? Deep habits, consumption shifts and transitory tax," Working Papers in Economics 701, University of Gothenburg, Department of Economics.

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